Journal ArticleDOI
The operator k-functor and extensions of c*-algebras
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In this paper, a general operator K-functor is constructed, depending on a pair A, B of C*-algebras, and the results (homotopy invariance, Bott periodicity, exact sequences) permit one to compute effectively in concrete examples.Abstract:
In this paper a general operator K-functor is constructed, depending on a pair A, B of C*-algebras. Special cases of this functor are the ordinary cohomological K-functor K*(B) and the homological K-functor K*(A). The results (homotopy invariance, Bott periodicity, exact sequences, etc.) permit one to compute effectively in concrete examples. The main result, concerning extensions of C*-algebras, consists in a description of a stable type of extensions of the most general form: . It is shown that the sum of such an extension with a fixed decomposable extension of the form is uniquely determined by an element of the group . Bibliography: 25 titles.read more
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Book
Operator Algebras: Theory of C*-Algebras and von Neumann Algebras
TL;DR: In this article, the authors present a model for operators on Hilbert Space, including C*-Algebras, Von Neumann Algebra, and K-Theory and Finiteness.
Journal ArticleDOI
Noncommutative geometry and reality
TL;DR: The notion of real structure in spectral geometry was introduced in this paper, motivated by Atiyah's KR•theory and by Tomita's involution J. It allows us to remove two unpleasant features of the Connes-Lott description of the standard model, namely, the use of bivector potentials and the asymmetry in the Poincare duality and in the unimodularity condition.
Classifying Space for Proper Actions and K-Theory of Group C*-algebras
TL;DR: In this paper, a reformulation of the conjecture is presented, which is simpler and applies more generally than the earlier statement. But the universal example for proper actions is not considered.
References
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Classification of injective factors
TL;DR: Nann et al. as mentioned in this paper presented a survey of the main lines of the investigation in the classification of factors, culminating in the Connes-Takesakl structure theory of type III factors.
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Inner Product Modules Over B ∗ -Algebras
TL;DR: In this article, the authors investigate right modules over a B*algebra B which posses a B-valued "inner product" respecting the module action, and show that such self-dual modules have important properties in common with both Hilbert spaces and W*-algebras.
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The completely positive lifting problem for C*-algebras
Man-Duen Choi,Edward G. Effros +1 more
TL;DR: In this article, it was shown that if A is separable, and either A, B/J, or B/B is contractive, the lifting problem for q is to determine whether or not one can find * so that the diagram commutes.